I am looking around for a good grease cutting dish soap that I can make at home. I am already making my own laundry soap, but I'm tired of needing to buy dish soap; and I've become sensitive to a lot of bar/liquid soaps that for bathing/shower purposes I have had to go no soap. Unfortunately after both me and my partner spent years working in food service we both have a strong desire to have them so well cleaned that we need to use some kind of soap product on the dishes.
Been there, Seen that, and have the post cards to prove it.
I've been making and selling soap for five years. The best liquid soap that you can make involves potasium hydroxide and an involved process that requires a bit of learning. I haven't tried yet although I have a pound of potasium hydroxide in my stash, and have had for several years. To get real grease cutting, you want a detergent. Not all detergents are the same; some come from natural, friendly coconut derived sources. However, they are pretty much drying to more or lesser degrees. You can do a bit of research to find some that are less so.
If you want skin friendly, I would maybe try a liquid soap with potasium (spelling, too tired to look up) hydroxide. The molecule structure makes the soap not solid like sodium hydroxide will do, but it is still, basically soap and therefore not very good with grease cutting. Adding orange oil will help.